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A Review Paper on Hough Transform and It's Applications in Image ISSN(Online): 2319-8753 ISSN (Print) : 2347-6710 International Journal of Innovative Research in Science, Engineering and Technology (An ISO 3297: 2007 Certified Organization) Vol. 5, Special Issue 13, October 2016 A Review Paper on Hough Transform and it’s Applications in Image Processing Biswajit Sit 1, Md. Iqbal Quraishi 2 P.G. Student, Department of Computer Science Engineering, Kalyani Govt. Engg. College, Kalyani, Nadia, India1 Assistant Professor, Department of Information Technology, Kalyani Govt. Engg. College, Kalyani, Nadia, India2 ABSTRACT: The Hough transform is a feature extraction method that can be used in image analysis and digital image processing. The aim of this technique is to produce a computer vision system that can detect arbitrary shapes within a sample image. The main purpose of this method is finding imperfect instances of objects within a certain class of shapes by a voting procedure. The classical Hough transform was mainly introduced for the identification of lines in images, but later the Hough transform has been modified and extended to identify the positions of arbitrary shapes within an image, most commonly the extended version indulged itself in finding circles or ellipses. In that case appropriate parametric representation is needed. Nowadays there are a wide range of areas where the Hough Transform can be implemented successfully such as in medical visualization or in order to achieve high accuracy in face recognition etc. The characteristics of Pupil and Iris under Uncontrolled illumination can also be obtained by Hough Circle Transform. In Objective Spinal Motion Imaging Assessment system (OSMIA), it is required to locate marker that can be used in determining the positions of the vertebral bodies. The measurement of vertebral motion has been a challenge to the field of biomechanics for many years but now several automatic approaches to these problems have been developed. The Hough Transform has also been introduced in morphological image processing to detect and estimate the number of red blood cells in the blood sample image. KEYWORDS: Hough Transform, Line detection, Medical visualization, Pupil detection, Vertebrae detection, Red blood cell estimation. I. INTRODUCTION The Hough transform is a kind of technique used in image processing for extracting the features of an image. It finds the imperfect instances of an object within a group of shapes by a voting procedure. This procedure is done in a parameter space, where object candidates are obtained as local maxima in an accumulator space that is explicitly constructed by the algorithm for computing the Hough transform. The Hough transform was invented by Richard Duda and Peter Hart in the year 1972, and they named it a "generalized Hough transform"[1] after the related 1962 patent of Paul Hough [2]. The transform got popularity in 1981 by Dana H. Ballard through a journal article titled "Generalizing the Hough transform to detect arbitrary shapes". The most common case of using the Hough transform is the linear transform for detecting straight lines in an image. In the image space, the straight line can be described as y = mx + c where the parameter m represents slope of the line, and c represents the y-intercept. This form of representation is called the slope-intercept model of a straight line. The main idea behind using Hough Transform is considering the features of the straight line not as discrete image points (x1, y1), (x2, y2), etc., but in terms of slope-intercept model. In general, the straight line y = mx + c can be denoted as a point (b, c) in the parameter space where b represents the slope of the line and c represents the intercept. However, problems arises in case of vertical lines as they are represented as x = a and would give rise to unbounded values of the slope parameter m. Thus for this computational phenomenon, Duda and Hart proposed using of a different pair of parameters, denoted by r and θ (theta), for the lines in the Hough transform. These two values taken together as a whole define a point in the polar coordinate. Copyright to IJIRSET www.ijirset.com 206 ISSN(Online): 2319-8753 ISSN (Print) : 2347-6710 International Journal of Innovative Research in Science, Engineering and Technology (An ISO 3297: 2007 Certified Organization) Vol. 5, Special Issue 13, October 2016 Figure 1: Slope-intercept model of straight line The parameter r represents the algebraic distance between the line and the origin, while θ is the angle of the vector. If the line is located above the origin, θ is simply the angle of the vector from the origin to this closest point. Using this form, the equation of the line can be written as Which can be rearranged to r = xcos θ + ysin θ .It is therefore possible to associate with each line of the image a pair (r, θ) which is unique if θ ϵ [0, π) and r ϵ R, or if θ ϵ [0, 2π) and r≥0. The (r, θ) plane is sometimes referred to as Hough space for the set of straight lines in two dimensions. This representation makes this transform very similar to the Radon transform. For an arbitrary point on the image space, e.g. (x0, y0), the lines that go through this point are the pairs (r, θ) with r (θ) = x0cos θ + y0sin θ, Where r (the distance between the line and the origin) is determined by θ ϵ [0, π) .If r is required to be positive, then θ must vary in [0,2π). In other words, θ is the angle of the vector from the origin and this closest point (if r ≠ 0), or the angle of the vector orthogonal to the line and pointing to the half upper plane (if r=0). The lines that goes through (x0, y0) are the r (θ) = |x0cos θ + y0sin θ|. These representations leads to a sinusoidal curve in the (r, θ) plane [3], which is unique to that point. If the curves corresponding to the points are superimposed, then the location in the Hough space where they crosses each other corresponds to a line in the original image space that passes through both points. To be more general, a set of points that form a straight line will produce sinusoid curves that cross at the parameters for that line. Thus, the problem to detect collinear points can be converted to the problem of finding concurrent curves. II. DIFFERENT HOUGH TRANSFORMS A.LINE HOUGH TRANSFORM: A suitable equation for describing a set of lines in a parametric form is: x cosθ + ysinθ = r Where r is the length of the normal from the origin to this line and θ is the orientation of r with respect to the X-axis. A suitable way of describing this presentation is described in the figure 2 which shows an object taken as an example and the figure 3 shows the parametric representation of a line. Copyright to IJIRSET www.ijirset.com 207 ISSN(Online): 2319-8753 ISSN (Print) : 2347-6710 International Journal of Innovative Research in Science, Engineering and Technology (An ISO 3297: 2007 Certified Organization) Vol. 5, Special Issue 13, October 2016 Figure 2: gradients of the example object Figure 3: parametric representation of a line When an image is analyzed the (x, y) parameters represents the well known pixels that are selected for analyzing. The pair of θ and r used for parametric representation is inserted into an accumulator. Another approach to think about this fact is that all the lines that go through the point (x, y) are transformed into parametric space (θ, r) and then the relevant cell is increased by 1.Each and every single point present in the accumulator corresponds to certain line in the image. As this accumulator is discrete in nature it only consists of a set of all possible lines in R2. It also corresponds to a set of sinusoid curves which intersects in some points. The white portions in the figure 4 show the intersection area. Figure 4: Hough transformed image A very useful thing of this algorithm is the robustness of this approach against noise and gaps present in the input image. This technique can be useful in real life applications such as in analyzing ultrasound images which contains some obvious noise that may causes problems in analyzing the features. B. CIRCLE HOUGH TRANSFORM: To use the Hough Transform for detecting circles a suitable parametric representation is required. A circle can be represented as: (x-ax) 2 + (y-ay) 2 = R2 Where (ax, ay) denotes the center of the circle and R is the radius of the circle. A 3D accumulator array is also Copyright to IJIRSET www.ijirset.com 208 ISSN(Online): 2319-8753 ISSN (Print) : 2347-6710 International Journal of Innovative Research in Science, Engineering and Technology (An ISO 3297: 2007 Certified Organization) Vol. 5, Special Issue 13, October 2016 required for these three parameters used in representing the parametric equation. On the other hand if the radius of the circle is known in advance then the accumulator becomes two dimensional. There is a very close similarity between the circle Hough Transform [4] and line Hough Transform but the difference come into existence where every set pixel proposes every circle that satisfies (ax, ay, R). If there are many such pixels Proposes a certain circle or lie on the same circle a peak arises and it can be detected in the accumulator using thresholding. This circle detection method can also be modified to identify other irregular shaped objects (e.g. ellipse) that can be represented in a parametric form. In that case the algorithm turns into a problematic one as the complexity of finding the object get increased.
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